Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World
In this paper we provide two simple new versions of Arrow’s impossibility theorem, in a model with only one preference profile. Both versions are transparent, requiring minimal mathematical sophistication. The first version assumes there are only two people in society, whose preferences are being aggregated; the second version assumes two or more people. Both theorems rely on assumptions about diversity of preferences, and we explore alternative notions of diversity at some length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to illustrate our points.
|Date of creation:||2008|
|Contact details of provider:|| Postal: Department of Economics, Brown University, Providence, RI 02912|
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- Marc Fleurbaey & Philippe Mongin, 2005.
"The news of the death of welfare economics is greatly exaggerated,"
- Marc Fleurbaey & Philippe Mongin, 2004. "The News of the Death of Welfare Economics is Greatly Exaggerated," Working Papers hal-00242931, HAL.
- Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
- Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
- Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
- Robert P. Parks, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 447-450.
- Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
- Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
- Robert A. Pollak, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 73-90.
- Abram Burk, 1938. "A Reformulation of Certain Aspects of Welfare Economics," The Quarterly Journal of Economics, Oxford University Press, vol. 52(2), pages 310-334.
- Kevin W. S. Roberts, 1980. "Social Choice Theory: The Single-profile and Multi-profile Approaches," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 441-450.
- Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328-328.
- Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 381-418, December.
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